Final answer:
The null hypothesis for each claim is stated as the status quo, with the alternative hypothesis representing the claim being tested. For election votes, the null is no majority, and the alternative is a majority. For pizza size and ibuprofen content, the nulls are at least 10 inches and exactly 250 mg respectively, with the alternatives being less than 10 inches and not equal to 250 mg.
Step-by-step explanation:
Constructing the null and alternative hypotheses is a crucial step in hypothesis testing. For the claim "I am going to get the majority of the votes to win this election," the null hypothesis (H0) would be the statement that you will not get the majority of votes, typically expressed as H0: p ≤ 0.5 where p represents the proportion of votes you would receive. The alternative hypothesis (Ha) would be that you will get the majority of the votes, or Ha: p > 0.5.
Regarding the claim "I suspect that your 10-inch pizzas are, on average, less than 10 inches in size," the null hypothesis would be H0: μ ≥ 10, which states that the average size of the pizzas is at least 10 inches (μ is the average pizza size). The alternative hypothesis would be Ha: μ < 10, suggesting that the average size is indeed less than 10 inches.
For the statement "I will have to fine the company since its tablets do not contain an average of 250 mpg of ibuprofen as advertised," the appropriate null hypothesis is H0: μ = 250, asserting that the average content of ibuprofen per tablet is 250 mg. The alternative hypothesis is Ha: μ ≠ 250, asserting that the average content is not 250 mg as claimed.